When Eric Hosmer aggravated a hand injury on July 24 and was deemed out for three to six weeks, the Royals figured to suffer in two ways: They would miss his resurgent bat and rangy Gold Glove fielding.

Naturally, they would be a poorer team for it.

Only it hasn’t played out that way.

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Instead, including the night Hosmer was hurt again, the Royals have won 12 of 14 (13 of 15 overall) and hold first place in the American League Central as they prepare for a weekend series at Minnesota.

There are many reasons for this, especially pitching and timely offense furnished from nearly every cranny of the lineup and bench.

But one reason that’s been pivotal has been the revitalization of Billy Butler … in a most direct correlation to Hosmer’s absence.

Butler had been flat much of the season, but his bat has come to life: In the last 14 days, he’s hitting .362 (17 of 48) with five doubles, two home runs and nine RBIs.

Only a few weeks after being benched and demoted in the lineup, Butler was last week’s AL player of the week.

Moreover, he’s been more than fine at first base, where he hadn’t played regularly for a few years and initially half-jokingly said his only goal was to go “unnoticed.”

The other day, he said he’s been working on fooling himself into thinking he wants the ball hit his way on every pitch.

“If you don’t do that, I don’t think you’re putting yourself into the best position to make the play,” he said, adding that even if he doesn’t have Hosmer’s scope and wingspan, “I can sure as heck set myself up” to make all plays he can get to.

However he’s approaching it, it’s working.

Other than the foul pop he botched in a lost Royals inning at Oakland, Butler has been flawless in the field and even has made a few notable scoops out of the dirt.

To hear him tell it, this all goes together.

Even though he’s had success as a designated hitter in the past, he believes that his slumps tend to perpetuate themselves when that’s all he does in a game since he’s apt to dwell on a bad at-bat.

Coincidence or not, the numbers bear that out.

When he’s at first base this season, Butler is 23 of 70 (.329) with seven doubles, three home runs and 12 RBIs.

That’s as many home runs as he has in 357 at-bats as the DH, where he’s hitting .261. (He also has a pinch-hit home run).

His career numbers are less distinct but still back up his suggestion:

In 372 games and 1,406 at-bats as a first baseman, Butler is hitting .306 with 43 home runs and 208 RBIs.

In just under twice as many games and at-bats (719, 2,744) as a DH, Butler is hitting .291 with 80 home runs and 399 RBIs.

None of this means he shouldn’t go back to DH when Hosmer returns, of course.

But it helps account for why the Royals have stayed not only viable but managed to become more dynamic since losing him.

2. Aoki A-OK?

Also suddenly surging to life some is outfielder Nori Aoki, who has eight hits in his last 16 at-bats and 10 of his last 23.

He’s still at just .272 for the season, but he’s now doing a lot more of what he was brought here for.

Earlier this week, manager Ned Yost said Aoki had been battling an issue all season. “Infamiliarity,” he called it, meaning unfamiliarity.

“It’s tough for players to change leagues,” Yost said.

Aoki came to the Royals following two years in Milwaukee, where he hit .288 and .286 after what might have been considered more of an adjustment … from playing in Japan.

But to make his point, Yost pointed to the case of Ted Simmons upon being traded from St. Louis to Milwaukee (then in the American League).

Simmons had hit over .300 six times in the previous 10 seasons with the Cardinals and hit “like .210” his first year with the Brewers, Yost said, before regaining some form.

Pretty close: Simmons hit .216 in 1981.

Yost said it was because he struggled to adjust to an entire array of pitchers he’d never seen.

“And that’s what it was for Nori,” he said, adding that now that Aoki has seen many pitchers two and three times “he’s much more comfortable and much more successful.”

3. Where Have You Gone, Joe DiMaggio?

Normally during the season, Yost might at least be seen in public at a Starbucks. But asked if outside Kauffman Stadium he’s witnessed any level of fan excitement about the first-place Royals, he said, “I don’t even go to Starbuck’s any more. At home, I got this new thing called ‘Mr. Coffee.’ Works really good.”

4. Still Bound For Infinity And Beyond

Had a long talk with former Chiefs coach Dick Vermeil the other day for some upcoming stories. Even at 77, even as he talks about his wine business (sales are up 55 percent), his energy still resonates over the phone.

Hearing his voice always makes me think about what one of my journalistic idols, Jim Thomas of the St. Louis Post-Dispatch, used to call him: Buzz Lightyear.

5. The Real Deal

There’s already a lot to like about what Kim Anderson is doing as Mizzou’s new men’s basketball coach, including how he’s barnstormed around the state, recruited and set a standard for work ethic with his team.

But it’s his authenticity that has and will mark Anderson’s tenure, and that’s showing up even in such details as the wording on news releases quoting him.

In short, when Mizzou puts out a statement from Anderson, you know it’s a statement from Anderson.

Here’s his latest, from when Mizzou dismissed forward Torren Jones last week for an unspecified violation of team rules:

“We have high standards at the University of Missouri and after consulting with (athletic director) Mike Alden, I have made the decision to dismiss Torren Jones from our program. I am disappointed in Torren’s actions and want to be very clear about the culture of accountability we are building within our program. It’s a privilege to wear the University of Missouri uniform, and we will represent our University and our state with great integrity.”

This might seem unremarkable. But even without getting into specifics, it’s much more blunt than most typically vanilla statements in such situations. And it speaks well for the type of imprint — and voice — he’s lending to the program already.